Information on Result #693066
Linear OA(2526, 390636, F25, 7) (dual of [390636, 390610, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(2525, 390626, F25, 7) (dual of [390626, 390601, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2517, 390626, F25, 5) (dual of [390626, 390609, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(259, 10, F25, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,25)), using
- dual of repetition code with length 10 [i]
- linear OA(251, 10, F25, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2526, 390636, F25, 2, 7) (dual of [(390636, 2), 781246, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (19, 26, 390636)-net over F25 | [i] | ||
| 3 | Linear OOA(2526, 195318, F25, 2, 7) (dual of [(195318, 2), 390610, 8]-NRT-code) | [i] | OOA Folding | |